674 Profs. Morley and Miller : Experiments to 



question cuts the line of motion in 2, and intersects the 

 mirror in e. The wave-front reflected from D at £ = will 

 have reached the point f l9 and the tangent ef ± establishes 

 the reflected wave-front. At the times 2r, 3r, &c, this 

 particular disturbance will be found at/^/s? A? & c « 



When D is at a position 2, a new disturbance will have 

 been established at g, which, at the time £ = 5t, will be found 

 at g 5 . In the same way, h 5 , i 5 , k b will have arranged them- 

 selves in the line / 5 h . At the time t = 10r the six wave- 

 fronts will have been reflected from I, and will be placed 

 along the line o 10 f 10 . The angle/^OIo is equal to the 

 aberration of the wave-fronts after reflexion from D. As, at 

 this azimuth, the angles of incidence and of reflexion at I 

 are equal, this angle is also the aberration of the emergent 

 rays. 



Part of the wave-front /, indicated by /', will be trans- 

 mitted through the mirror D. It will overtake the mirror 

 II at the time t — 8t, when II will have position marked 



11 8 , fig. 7. Returning after reflexion, it will take the posi- 

 tion noted for the times t = 9r, t = 10r ; and meeting the 

 mirror D at £ = 10§r, it will be reflected as shown to/'n, at 

 an angle whose tangent is given by the formula below. The 

 following wave-front g' will be reflected one period later, at 



11 9 , and it is shown in several positions. The wave-front/, 

 belonging to the other system, having passed through the 

 mirror, and having reached the line, Sd, at £=10r, is shown 

 at/ al . 



In fig. 8 is shown the position of the wave-fronts below 

 the mirror D for the time £=15r. f Vo and/ ' 13 have moved 

 along the paths indicated, while the other wave-fronts have 

 moved in a corresponding manner, their position at the time 

 t = 15r being as shown in the figure. The wave-fronts of 

 the unaccented system are placed on the line op ; the aber- 

 ration of the system is equal to the angle 8. The wave- 

 fronts of the accented system are placed on the line qr ; the 

 corresponding aberration is the angle 8'; the line T Yo q being 

 the position of the axis of the observing telescope at the time 

 £ = 15t. Produce the planes of the wave-fronts, draw lines 

 I, /', parallel to gT 15 , the axis of the telescope, each terminated 

 by the planes of consecutive wave-fronts. Their lengths 



\ A/ 



are /= ^ , l f = ~, . It is to be proved that 1=1'. 



cos o cos o 



Putting <f> for the angle of incidence and $' for the angle 



of reflexion, we have for both reflexions at D, = 45°. For 



this azimuth there is no change of angles at I and II. The 



